Connections between the generalized marcum Q-function and a class of hypergeometric functions

IEEE Transactions on Information Theory

Volumn 60, Issue 2, 2014, Pages 1077-1082

  Morales Jimenez, David ^a   Lopez Martinez, F Javier ^b   Martos Naya, Eduardo ^c   Paris, Jose F ^c   Lozano, Angel ^a  

^a UNIVERSITAT POMPEU FABRA   (Spain)

^b STANFORD UNIVERSITY   (United States)

^c UNIVERSITY OF MÁLAGA   (Spain)

Author keywords

bivariate Nakagami m; confluent hypergeometric functions; Marcum q function; minimum eigenvalue distribution; non central Wishart matrix

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; INFORMATION THEORY;

CONFLUENT HYPERGEOMETRIC FUNCTIONS; MARCUM-Q FUNCTION; MINIMUM EIGENVALUE; NAKAGAMI-M; WISHART MATRICES;

COMMUNICATION;

EID: 84893491688     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2013.2291198     Document Type: Article

References (38)

1. G. Di Blasio and A. Neri, "Modified Q-functions and their use in detection analysis," IEEE Trans. Inf. Theory, vol. 37, no. 4, pp. 1123-1142, Jul. 1991. (Pubitemid 21674984)
2. A. Baricz and Y. Sun, "New bounds for the generalized Marcum Q-function," IEEE Trans. Inf. Theory, vol. 55, no. 7, pp. 3091-3100, Jul. 2009.
3. G. Corazza and G. Ferrari, "New bounds for the Marcum Q-function," IEEE Trans. Inf. Theory, vol. 48, no. 11, pp. 3003-3008, Nov. 2002. (Pubitemid 35327614)
4. V. M. Kapinas, S. K. Mihos, and G. K. Karagiannidis, "On the monotonicity of the generalized Marcum and Nuttall Q-functions," IEEE Trans. Inf. Theory, vol. 55, no. 8, pp. 3701-3710, Aug. 2009.
5. Y. Sun, A. Baricz, and S. Zhou, "On the monotonicity, log-concavity, and tight bounds of the generalized Marcum and Nuttall Q-functions," IEEE Trans. Inf. Theory, vol. 56, no. 3, pp. 1166-1186, Mar. 2010.
6. G. Alfano, A. De Maio, and A. Tulino, "A theoretical framework for LMS MIMO communication systems performance analysis," IEEE Trans. Inf. Theory, vol. 56, no. 11, pp. 5614-5630, Nov. 2010.
7. R. W. Heath and D. J. Love, "Multimode antenna selection for spatial multiplexing systems with linear receivers," IEEE Trans. Signal Process., vol. 53, no. 8, pp. 3042-3056, Aug. 2005. (Pubitemid 41372814)
8. P. Dharmawansa and M. R. McKay, "Extreme eigenvalue distributions of some complex correlated non-central Wishart and gamma-Wishart random matrices," J. Multivariate Anal., vol. 102, no. 4, pp. 847-868, Jan. 2011.
9. D. Morales-Jimenez, J. Paris, and A. Lozano, "Outage probability analysis for MRC in ?-? fading channels with co-channel interference," IEEE Commun. Lett., vol. 16, no. 5, pp. 674-677, May 2012.
10. F. Chatelain, J. Y. Tourneret, J. Inglada, and A. Ferrari, "Bivariate gamma distributions for image registration and change detection," IEEE Trans. Image Process., vol. 16, no. 7, pp. 1796-1806, Jul. 2007. (Pubitemid 47018877)
11. F. J. Lopez-Martinez, D. Morales-Jimenez, E. Martos-Naya, and J. F. Paris, "On the bivariate Nakagami-m cumulative distribution function: Closed-form expression and applications," IEEE Trans. Commun., vol. 61, no. 4, pp. 1404-1414, Apr. 2013.
12. R. Narasimhan, "Spatial multiplexing with transmit antenna and constellation selection for correlated MIMO fading channels," IEEE Trans. Signal Process., vol. 51, no. 11, pp. 2829-2838, Nov. 2003.
13. G. Burel, "Statistical analysis of the smallest singular value in MIMO transmission systems," in Proc. WSEAS ICOSSIP, 2002, pp. 1-6.
14. M. K. Simon and M.-S. Alouini, Digital Communications over Fading Channels, 2nd ed. New York, NY, USA: Wiley, 2005.
15. C. Tan and N. Beaulieu, "Infinite series representations of the bivariate Rayleigh and Nakagami-m distributions," IEEE Trans. Commun., vol. 45, no. 10, pp. 1159-1161, Oct. 1997. (Pubitemid 127827356)
16. J. Reig, L. Rubio, and N. Cardona, "Bivariate Nakagami-m distribution with arbitrary fading parameters," Electron. Lett., vol. 38, no. 25, pp. 1715-1717, Dec. 2002.
17. R. de Souza and M. Yacoub, "Bivariate Nakagami-m distribution with arbitrary correlation and fading parameters," IEEE Trans. Wireless Commun., vol. 7, no. 12, pp. 5227-5232, Dec. 2008.
18. N. Beaulieu and K. Hemachandra, "Novel simple representations for Gaussian class multivariate distributions with generalized correlation," IEEE Trans. Inf. Theory, vol. 57, no. 12, pp. 8072-8083, Dec. 2011.
19. A. A. Abu-Dayya and N. C. Beaulieu, "Analysis of switched diversity systems on generalized-fading channels," IEEE Trans. Commun., vol. 42, no. 11, pp. 2959-2966, Nov. 1994.
20. W. C. Jakes, Microwave Mobile Communications. New York, NY, USA: IEEE Press, 1974.
21. M. Zorzi, R. Rao, and L. Milstein, "Error statistics in data transmission over fading channels," IEEE Trans. Commun., vol. 46, no. 11, pp. 1468-1477, Nov. 1998. (Pubitemid 128739497)
22. H.-S. Wang and P.-C. Chang, "On verifying the first-order Markovian assumption for a Rayleigh fading channel model," IEEE Trans. Veh. Technol., vol. 45, no. 2, pp. 353-357, May 1996. (Pubitemid 126772693)
23. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 6th ed. San Diego, CA, USA: Academic, 2000.
24. A. Erdelyi, High Order Transcendental Functions, vol. 1. New York, NY, USA: McGraw-Hill, 1953.
25. J. Marcum, "Table of Q functions," Rand Corp., Santa Monica, CA, USA, Tech. Memo. M-339, Jan. 1950.
26. A. Nuttall, "Some integrals involving the QM function (Corresp.)," IEEE Trans. Inf. Theory, vol. 21, no. 1, pp. 95-96, Jan. 1975.
27. C. O'Driscoll and C. Murphy, "A simplified expression for the probability of error for binary multichannel communications," IEEE Trans. Commun., vol. 57, no. 1, pp. 32-35, Jan. 2009.
28. M. Schwartz, W. R. Bennett, and S. Stein, Communication Systems and Techniques. New York, NY, USA: IEEE Press, 1966.
29. Y. Chen and S. Manning, "Some eigenvalue distribution functions of the Laguerre ensemble," J. Phys. A, Math. General, vol. 29, no. 23, pp. 7561-7579, 1999.
30. M. Chiani, M. Win, and A. Zanella, "On the capacity of spatially correlated MIMO Rayleigh-fading channels," IEEE Trans. Inf. Theory, vol. 49, no. 10, pp. 2363-2371, Oct. 2003.
31. P. Forrester, "Eigenvalue distributions for some correlated complex sample covariance matrices," J. Phys. A, Math. Theoretical, vol. 40, no. 36, pp. 11093-11103, Sep. 2007.
32. A. Maaref and S. Aissa, "Joint and marginal eigenvalue distributions of (non)central complex Wishart matrices and PDF-based approach for characterizing the capacity statistics of MIMO Ricean and Rayleigh fading channels," IEEE Trans. Wireless Commun., vol. 6, no. 10, pp. 3607-3619, Oct. 2007. (Pubitemid 47625165)
33. A. Zanella, M. Chiani, and M. Win, "On the marginal distribution of the eigenvalues of Wishart matrices," IEEE Trans. Commun., vol. 57, no. 4, pp. 1050-1060, Apr. 2009.
34. S. Jayaweera and H. Poor, "On the capacity of multiple-antenna systems in Rician fading," IEEE Trans. Wireless Commun., vol. 4, no. 3, pp. 1102-1111, May 2005. (Pubitemid 40683178)
35. Y. Zhu, P.-Y. Kam, and Y. Xin, "On the mutual information distribution of MIMO Rician fading channels," IEEE Trans. Commun., vol. 57, no. 5, pp. 1453-1462, May 2009.
36. D. Gore, R. Heath, and A. Paulraj, "Statistical antenna selection for spatial multiplexing systems," in Proc. IEEE ICC, vol. 1. May 2002, pp. 450-454. (Pubitemid 34631888)
37. J. H. Stock and M. Yogo, Testing for Weak Instruments in Linear IV Regression. Cambridge, MA, USA: NBER, Nov. 2002.
38. J. Proakis, Digital Communications, 4th ed. New York, NY, USA: McGraw-Hill, Aug. 2000.